Chapter A.8, Problem 21AYU

To determine

To find: The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $\$5$ per pound with some Orange Pekoe tea that sells for $\$3$ per pound to get 100 pounds of the new blend. The selling price of the new blend is to be $\$4.50$ per pound, and there is to be no difference in revenue between selling the new blend and selling the other types.

Answer to Problem 21AYU

75 pounds of Earl Grey tea with 25 pounds of Orange Pekoe needed.

Explanation of Solution

Let $a=$ pounds of Earl Grey needed.

Let $b=$ pounds of Orange Pekoe needed.

$a+b=100$

$\frac{5a+3b}{100}=4.50$

That is $5a+3b=450$.

Therefore solving these two equation $a+b=100$ and $5a+3b=450$ we get,

$2a=150$. That is $a=75, b=25$.

Therefore, 75 pounds of Earl Grey tea with 25 pounds of Orange Pekoe needed.